Finite Group DatabasebetaFinite Group Databasebeta| order | 23126 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D373⋊C31 |
| unambiguous semidirect product | (C373⋊C31)⋊C2 |
| Fitting, socle, derived, Sylow | C373 ⋊ C2×C31 |
| Hall | C373⋊C31 ⋊ C2 |
| Hall | D373 ⋊ C31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C373 | C2×C31 |
| LCS | G ▷ C373 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 373 |
Polycyclic presentation:
2,31,373|c^a=c^372,c^b=c^36668 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23126, 1);